A359389 Maximal coefficient of Product_{k=1..n} (1 + 2*x^k).

1, 2, 4, 8, 16, 32, 72, 176, 384, 976, 2496, 6560, 17152, 45952, 123520, 336640, 920832, 2526976, 6979584, 19379712, 53966336, 150892544, 423132160, 1190260736, 3356964864, 9491228672, 26889519104, 76351971328, 217229369344, 619159953408, 1767696515072, 5054679908352

Offset: 0

Author

Vaclav Kotesovec, Dec 29 2022

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A025591, A032302, A160235.

Programs

Mathematica

Table[Max[CoefficientList[Product[1 + 2*x^k, {k, 1, n}], x]], {n, 0, 40}]
p = 1; Join[{1}, Table[p = Expand[p*(1 + 2*x^n)]; Max[CoefficientList[p, x]], {n, 1, 40}]]

PARI

a(n) = vecmax(Vec(prod(k=1, n, 1 + 2*x^k))); \\ Michel Marcus, Dec 29 2022

Formula

a(n) ~ 3^(n + 3/2) / (2*sqrt(Pi)*n^(3/2)).